From our scaling analyses we see that \(V_E\)  corresponds to the \(d=1\)  case.
Meanwhile, for the spin-spin term in \(V_{\rm M}\)  we usually use the expression from the Fermi-Breit-Pauli interaction [1]}, [2]},
\(V_{s, {\rm trad} } (r) = \frac{\, \alpha _s \,}{\, m_1 m_2 \,} \, 2\pi \delta (\vec{r}) \,.\) 
